Universal self-assembly of one-component three-dimensional dodecagonal quasicrystals

Abstract

Using molecular dynamics simulations, we study computational self-assembly of one-component three-dimensional dodecagonal (12-fold) quasicrystals in systems with two-length-scale potentials. Existing criteria for three-dimensional quasicrystal formation are quite complicated and rather inconvenient for particle simulations. So to localize numerically the quasicrystal phase, one should usually simulate over a wide range of system parameters. We show how to universally localize the parameter values at which dodecagonal quasicrystal order may appear for a given particle system. For that purpose, we use a criterion recently proposed for predicting decagonal quasicrystal formation in one-component two-length-scale systems. The criterion is based on two dimensionless effective parameters describing the fluid structure which are extracted from the radial distribution function. The proposed method allows reduction of the time spent for searching the parameters favoring a certain solid structure for a given system. We show that the method works well for dodecagonal quasicrystals; this result is verified on four systems with different potentials: the Dzugutov potential, the oscillating potential which mimics metal interactions, the repulsive shoulder potential describing effective interactions for the core/shell model of colloids and the embedded-atom model potential for aluminum. Our results suggest that the mechanism of dodecagonal quasicrystal formation is universal for both metallic and soft-matter systems and it is based on competition between interparticle scales.

Anomalous behavior and structure of a liquid of particles interacting through the harmonic-repulsive pair potential near the crystallization transition

“…The most marked change observed in the scaled PDF, as pressure increases, is the splitting of its first PDF peak into two sub-peaks (this behavior, of course, is observed in the unscaled PDF also). Similar splitting is often observed in two-length-scale systems where different bond lengths are generated by the special form of the interparticle potentials, like the two attractive wells or the repulsive shoulder, and so on 37,[40][41][42] . Note, that the same effect was observed in star polymers solutions modeled by the ultrasoft potential consisting of two parts: the logarithmic repulsion at r < σ and the exponential Yukawa-like tail at r > σ , where σ is the characteristic corona diameter 10,11,43 .…”

Crystalline structures of particles interacting through the harmonic-repulsive pair potential

“…Alternatively, one can also think that each column is formed by 3 (three) helical coils such that the full pitch of every coil involves 7 (seven) particles. From this perspective, the observed structure resembles locally the organization of particles in some columnar quasicrystals [33,34,[36][37][38]. 50 Table VI.…”

“…Discovery of quasicrystals lead, in particular, to the systematic studies of the single component systems consisting of the particles interacting through sphericallysymmetric pair potentials whose shape is more complex than the shape of the simple "traditional" pair potentials [28][29][30][31][32][33][34][35][36][37][38]. The goal of the related studies is often to clarify the relationship between the shape of the potential and the structural/dynamic properties of the systems of particles interacting through such potentials.…”

Inverse design of self-assembling Frank-Kasper phases and insights into emergent quasicrystals

“…It is recognized that quasicrystal formation (and presumably, by extension, that of their periodic approximants) in single-component systems requires two lengthscales in the interaction potential. [74][75][76] In Fig. 4, it is clear that those two lengthscales function to 1) allow for interparticle separations of r ≈ d while 2) penalizing intermediate interparticle distances characteristic of most lattices.…”